Emergent Bloch excitations in Mott matter

We develop a unified theoretical picture for excitations in Mott systems, portraying both the heavy quasiparticle excitations and the Hubbard bands as features of an emergent Fermi liquid state formed in an extended Hilbert space, which is nonperturbatively connected to the physical system. This observation sheds light on the fact that even the incoherent excitations in strongly correlated matter often display a well-defined Bloch character, with pronounced momentum dispersion. Furthermore, it indicates that the Mott point can be viewed as a topological transition, where the number of distinct dispersing bands displays a sudden change at the critical point. Our results, obtained from an appropriate variational principle, display also remarkable quantitative accuracy. This opens an exciting avenue for fast realistic modeling of strongly correlated materials.

Figure 1

Representation of a lattice including two ghost orbitals ($\alpha =2,3$). The Hamiltonian of the system acts as 0 over the auxiliary ghost degrees of freedom. The Hubbard interaction $U$ acts only on the physical orbital $\alpha =1$.

Figure 2

Evolution of (top) total energy, (middle) local double occupancy, and (bottom) QP weight as a function of the Hubbard interaction strength $U$ for the single-band Hubbard model with semicircular DOS at half-filling. The ghost-GA results are shown in comparison with the ordinary GA and with DMFT+NRG. The ghost-GA boundaries of the coexistence region $U_{c1},U_{c2}$ are indicated by vertical dotted lines. Inset: Integral of ghost-GA local spectral weight over all frequencies (see discussion in main text).

Figure 3

Poles of the ghost-GA energy-resolved Green's function (bullets), see Eq. (6), in comparison with DMFT+NRG. The size of the bullets indicates the spectral weights of the corresponding poles. Metallic solution for $U=1,2.5$ and Mott solution for $U=3.5,5$.